Picking winners in electoral contests is a popular sport in Germany, as in many places elsewhere. During the 2002 campaign for the Bundestag, pre-election polls tracked the horse race of party support almost daily. Election junkies were invited to enter online sweepstakes. They could also bet real money, albeit in limited quantity, on the parties' fortunes on WAHL$TREET, a mock stock market run by Die Zeit and other media. As usual, election night witnessed the race of the networks to project the winner the second the polls where voters had cast their ballots closed. But in 2002, there was also one newcomer in the business of electoral prophecy: a statistical forecast based on insights from electoral research.

Three months before the date of the 2002 Bundestag election, we issued a vote forecast based on a model that was published two years earlier. (1) Our prediction was that the coalition parties in office would win the Bundestag election on September 22. SPD and Greens, so the forecast first publicized by dpa on June 23 and confirmed on August 24, were going to get 47.1 percent of the vote. (2) That would be enough, we said, to defeat the combination of CDU/CSU and FDP, provided all other parties mustered at least 6 percent of the vote. The prediction proved to be a forecaster's dream come true. Not only did the red-green coalition win the election, but the actual vote of those two parties matched our forecast right down to the decimal point. And all that occurred against extremely long odds as set by opinion polls.

To offer a forecast based on a few predictors of the vote was a novel experience in Germany. And while some novelties are swept up eagerly, this one was greeted with a mix of bewilderment, disbelief, and outright disdain. The attempt of forecasting an election outcome struck many as simple-minded, if not altogether wrongheaded; as more an exercise in astrology than astronomy. The only thing certain was the belief that the forecast would badly miss its target. One critic gleefully predicted that our "model will not survive the next [2002] election." (3) In June and through much of the summer, of course, polls showed the governing parties trailing far behind and headed for certain defeat. So was it just luck, as detractors claimed afterwards, that our forecast model "survived" the 2002 election? No doubt, getting it dead right was a stroke of luck. That is a once-a-life-time experience for a forecaster. But having a model that gets the outcome right almost every time and comes close to the margin of victory is not simply a case of luck. What is the Zauberformel, or magic formula, as the German media teasingly referred to our forecast model? How did we design it? What are its scientific qualifications? And how has the formula fared in previous Bundestag elections?

No magic trick at all, our forecast formula combines predictors of the vote that are familiar to students of elections in Germany as well as elsewhere. We owe a special debt to forecast models of American elections. (4) Yet our formula should not be mistaken for a German replica of an American model. The predictors of out forecast model for Bundestag elections, in a nutshell, are long-term partisanship (a normal-vote baseline), short-term chancellor approval, and a medium-term dynamic of declining incumbent support over time, call it the "cost of ruling" or simply government fatigue. Using election returns and measures from opinion surveys, going as far back as 1953, we estimated the statistical influence of those variables on the vote in Bundestag elections. Forecasts after the fact confirmed that the model would have been capable of predicting German election outcomes from 1953 to 1998 with an average error of no more than 1.5 percent and picking the right winner each time. Given that track record, getting the winner right in 2002 should not really be all that surprising. More puzzling perhaps is why the 2002 pre-election polls varied so much when the outcome was so predictable. (5) We will offer some speculations on this puzzle at the end, but the final resolution must come from the organizations that poll vote intentions and from the media that report the electoral horse race.

The Forecast Target

Whoever tries to forecast the outcome of an election has to settle first on what exactly it is that is being forecast. The vote shares of all parties? That is what the pre-election polls aim to supply with samples of the total electorate, at least for parties above a minimum threshold of support. Here the quality of the forecast is measured by the average absolute deviation of the actual vote shares from the ones reported in the polls. This is a competition that a forecast model like ours cannot enter. Electoral research has a tough enough time with the analysis of vote choices in a two-party setting. We do not know of any model of voting that can determine with sufficient precision how voters make up their minds in a setting with five relevant political parties. This is not the place to fill this lacuna.

Our effort focuses on the politically most telling combination of parties: the parties forming the government before the election. Proportional representation and the resulting multiparty system in Germany have not prevented the creation of stable alignments of parties in and out of government. Politics in Berlin (and previously Bonn) is coalition politics. The electoral process and the policy making process in Germany are joined at the hip by a simple rule: a governing coalition whose parties obtain a majority of seats in an election continues in office, while a coalition that fails in that objective is replaced by another one. Some exceptions notwithstanding, this is a rule that offers valuable guidance for students of German elections. It transforms an unwieldy set of party alternatives into a handy dichotomy of incumbent versus non-incumbent parties. This is not only practical but also theoretically sound, as we argue below.

For each Bundestag election since 1949, we obtained the combined vote of the governing parties. Not included was the vote of any party that belonged to the government at some time during the term preceding the election but that departed before election day. Except for two elections, we were able to ascertain the incumbent vote …